Tool turrets of this kind are state of the art, as in DE 41 16 774 C1. The operational reliability of machine tools equipped with such tool turrets is to a large degree dependent on the functional reliability of the locking of the turret head. The reliability of the tooth system engagement is particularly inadequate when limited activation force is available for the movement of the locking part formed as a pressure piston, because, for example, for a large effective piston surface of the locking part, as is required for a pneumatic activation, adequate space is not available. In order to ensure reliable locking in spite of low activation force with a limited effective piston surface, the above-mentioned known solution envisages a special tooth form of the tooth system, with a small flank angle and a trapezoidal cross section form of the teeth. This solution is unsatisfactory in particular because that tooth form threatens the reliability of the tooth system engagement due to possible head-to-head contact.